Morphology Trajectory Integrity
Durability claims are valid only if morphology trajectory is continuous, observable, and bounded.
Doctrine Statement
In trajectory-sensitive polymer systems, durability claims are valid only if the morphology trajectory is explicitly accounted for, continuous, and bounded within validated limits.
Endpoint-only or discontinuous representations are non-admissible.
Trajectory Integrity Requirement
A valid trajectory must satisfy three conditions:
- Continuity across the full exposure history
- Direct observability of morphology parameters
- Bounded evolution within validated state space
Violation of any condition invalidates the claim.
The Missing Quantity
The governing variable is the evolving distribution of internal configurational free energy states.
This includes:
- Free volume distribution
- Entanglement stress fields
- Interfacial cohesion
- Defect populations
This distribution cannot be reduced to scalar endpoint properties.
Continuity Failure
Trajectory integrity is broken when:
- Measurement gaps exist in the trajectory
- Intermediate states are inferred rather than observed
- Exposure sequences are partially or ambiguously defined
Interpolated or assumed trajectories are not admissible representations.
Non-Commutativity as Integrity Test
Load order must be explicitly tested or bounded.
Failure to address order effects constitutes trajectory ambiguity and invalidates claims.
Irreversible Loss of Integrity
- Crossing non-recoverable morphology thresholds
- Path-dependent drift without reset pathway
- Loss of mapping between morphology and performance
Once integrity is lost, prior claims cannot be extended or reused.
Invariant Framework
G: Morphology-preserving transformations
Q: Material identity
S: Continuous morphology trajectory
Failure: discontinuity, interpolation, or collapse of trajectory into endpoints
Claim Eligibility Boundary
Any durability claim that relies on incomplete, interpolated, or discontinuous trajectories is invalid.
Observability and continuity are required—not optional.
Boundary Judgment
A trajectory that is not fully observed is not a trajectory—it is an assumption. Durability claims built on assumed trajectories exceed their epistemic authority.